Lawn care is relatively simple: water, mow, and fertilize. If you are doing those three things properly, you will rarely need to dethatch or use herbicide, fungicide, insecticide. As it happens, at least parts of your lawn have disease. The yellow/brown spots on the blades in the close up pictures tell the story. Usually too much water is the cause of disease, so let's talk about watering. Ideally you should water deeply and infrequently. Deep means 1 inch all at one time. Infrequently varies with the circumstances, but generally the air temperature is the dominant circumstance. When it is hot you should water more frequently than when it is cool. The range of frequency generally goes from monthly in the cool months to once per week in the hottest heat of summer. You don't live in the hottest parts of the world, so once per week should be the very maximum for you. I do live in a warm climate and can often go 2 weeks without watering. The grass may look wilted, but it is not dead. Your northern lawn will be different, but not that much.

Here's what I would do if I inherited that lawn as is. I would get the watering right. If you are watering more frequently than once per week you might have to wean the lawn out of that pattern by watering more deeply and less often until you are getting one inch all at one time. Measure 1 inch using cat food or tuna cans placed around the yard. Time how long it takes to fill them all and remember that time. Use that time from now on. Mow at the mower's highest setting. Fertilize right now with an organic fertilizer. If your father has used organic fertilizers in the past then you are in better shape than I'm thinking, but most people are so stuck on chemical fertilizers that they completely overlook the organics. The deep watering and organic fertilizer at least once per year will go a long way to repairing tired soil. You absolutely do not need to bring in more topsoil. In fact it may be that your father has been topdressing over the years and has built up too much topsoil already. If you ever decide to do a full renovation, consider whether you need to haul an inch or more of the topsoil away. For now just get the grass growing.

It will take a full 3 weeks to see improvement with the organic fertilizer, so use it soon. What you are looking for is improved color, growth, and grass density. If the diseased areas seem to be spreading quickly, then you will have to get a fungicide down to save the lawn, but I would resist that if at all possible. If the disease seems to be stable in one area, then just keep an eye on it until the organic fertilizer is working. Once the general health of the overall lawn is better, then consider the fungicide in the bad spots.